Abstract

The particle‐wave interaction to arbitrary order in perturbation theory is investigated for a weakly turbulent plasma in the presence of a uniform magnetic field. It is found that to every order in perturbation theory, the ensemble average distribution function obeys a diffusion equation in space. By conservation of energy and momentum between waves and particles, the growth or damping rate to any order may be determined. The damping rate for nonlinear cyclotron damping, the particle energization rate from very low‐frequency turbulence, and the growth rate for a nonlinear instability are calculated.